All natural numbers from 1 to 1000 were written in the following order: first, the numbers whose sum of digits is 1 were written out in ascending order, then, also in ascending order, the numbers with the sum of digits 2, then the numbers whose sum of digits is 3, etc. In what place was the number 996?

Leaflet #reverse_course

In the classroom of the math club, all the children who went there were given chocolates. The first visitor was given one chocolate bar and a tenth of all the remaining ones, the second visitor was given two chocolates and a tenth of the remaining ones, ..., the ninth visitor was given nine chocolates and a tenth of the remaining ones. After that, Sheldon came running, but, unfortunately, the chocolates were already over. How many chocolates did the children get?

Leaflet #reverse_course

There are 20 one-dollar coins and 20 half-dollar coins in the piggy bank. What is the smallest number of coins to take out of the piggy bank so that
1) two identical coins are sure to be among them?
2) two one-dollar coins are sure to be among them?
3) two different coins are sure to be among them?

Leaflet #money

Two hostesses bought milk every day for a month. The price of milk varied daily. The average price of milk for the month was $4. Each day the first hostess bought one gallon, and the second bought $4 worth of milk. Which one spent more money during that month and which one bought more milk?

Leaflet #money

There are nine coins, among them one counterfeit. The real coins all weigh the same, but the fake one weighs a little less. How can you use a cup scale without arrows and weights to determine a counterfeit coin in two weighings?

Leaflet #money

Pinocchio planted a money tree, and instead of leaves, gold coins appeared on it every day. The first day one coin appeared on the tree, the second day two, the third day three, and so every day it grew one more coin than the previous day. On the night of the 29th to the 30th day, Alice the Fox and Basilio the Cat came and ripped off all the gold coins. How many coins did the treacherous Alice and Basilio get?

Leaflet #money

The young man agreed to work on the condition that at the end of the year he would receive a Ford F-150 and $26,000. But at the end of 8 months, he quit his job and received a Ford F-150 and $10,000. How much was the Ford F-150 worth?

Leaflet #money

Two people play a game like this. They take turns putting the same coins on the round table. You can't put coins on top of each other. The loser is the one who has nowhere to put the next coin. Which player is guaranteed to win: the beginner or his opponent? How should he play?

Leaflet #money

There are coins on the table. Fifteen of them are eagle up and the rest are eagle down. Blindfolded, you have to put these coins into two piles so that the number of coins lying eagle up in these piles is the same. The number of coins in the piles can be different (the pile can consist of any number of coins, including one or even less), the coins can be turned over, but it is impossible to determine by touch how a coin lies.

Leaflet #money

Cut the square into a) 4; b) 9; c) 17 squares.

Leaflet #cut

Four dwarfs inherited from their uncle an orchard enclosed by 16 matchsticks with 12 fruit trees. The location of the trees is shown in the drawing. Divide the garden using 12 matches into four equal parts containing an equal number of trees each. The matches are only allowed to be placed on the dotted lines. (Equal parts must have the same shape, size, and same arrangement of trees.)

Leaflet #cut

The watermelon was cut into 4 parts and eaten. It turned out five crusts. How could this be?

Leaflet #cut

Cut the figure shown in the figure into four equal parts.

Leaflet #cut

The square napkin was folded in half, the resulting rectangle was folded in half again. The resulting square was cut with scissors in a straight line. Could the napkin fall apart
a) into 2 parts?
b) into 3 parts?
c) into 4 parts?
d) into 5 parts?

Leaflet #cut

Cut the figure shown in the figure into four identical parts so that they can be folded into a 6×6 square with a chess coloring.

Leaflet #cut

1) Cut a rectangle 4×9 in two parts, from which you can add a square 6×6.

2) Cut a rectangle 9×16 in two parts, which can be folded into a square.

Leaflet #cut

Cut each of the following figures into two equal parts.

Leaflet #cut

Eight rabbits were put in seven cages. Prove that there is a cage in which there are at least two rabbits.

Leaflet #pigeonhole

More about the pigeonhole principle

A team of four received 10 candies for winning the math regatta. The children divided the candies among themselves without breaking them. Determine whether the following statements are true:
a) "someone got at least two sweets";
b) "someone got at least three sweets";
c) "two people got at least two sweets";
d) "everyone got at least one sweets".

Leaflet #pigeonhole